But a U.N. official cast doubt on the claim and said it was confident security would be maintained for the country's long-delayed polls, now set for July 30.
The suspects arrested Tuesday were former soldiers who worked for a Congolese security agency, Interior Minister Theophile Mbemba said.
Mbemba said the men were arrested with military gear, but did not provide further details about the number or type of weapons, the AP reports.
They "were working in Kinshasa as security guards but it is clear that they were military personnel with political plans," Mbemba said. "They were part of a coup attempt, and they will face justice in Congo."
The United Nations said it could not confirm Congo's allegations.
Separately Wednesday, hundreds of demonstrators marched in Kinshasa to protest the delay of the election - originally to be held by June 30 - and the government's refusal to reopen voter rolls for the registration of opposition supporters who had planned to boycott the vote but later changed their minds.
The South African ambassador said 19 of those arrested had South African papers. It was not immediately possible to resolve the discrepancy between that and Mbemba's figure of 12. Ambassador Sisa Ngamane said the country had sent identification papers to the authorities for these men and that it expected to be included in the investigation.
Russia has deployed two armies and three units of Airborne Forces to its western borders as part of a verification check, Russian Defense Minister Sergei Shoygu said